If f−1, the inverse of f, is the function that "undoes" f and it is given that f(a)=b, find f−1(b).
Solution:
The inverse function undoes whatever f does: if y=f(x), then f−1(y)=x. Substituting a and b for x and y yields: if b=f(a), then f−1(b)=a.
Since we are given that f(a)=b, we must have
f−1(b)=a.
Function Theory (Lesson 5/5)
Inverse Functions
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Discussion
If f−1, the inverse of f, is the function that "undoes" f and it is given that f(a)=b, find f−1(b).
Solution:
The inverse function undoes whatever f does: if y=f(x), then f−1(y)=x. Substituting a and b for x and y yields: if b=f(a), then f−1(b)=a.